Finite Group Databasebeta

← Group #11772591

Character table — Group #11772591

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444444444444444444444488888888888888888888242424242424242424242424242424242424242424242424363636367272
order1244233466121212122223444666666666121212121212121212126666666666121212121212121212128888888824242424242424242424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1
χ6111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111
χ7111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111
χ8111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1
χ911-1-1111-111-1-1-1-111-11-11-11111-1-1111-1-1-1-1-1-111-1-1111-11111-1-1-1-11-1-1-111-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−iii−i−ii−i
χ1011-1-1111-111-1-1-1-111-11-11-11111-1-1111-1-1-1-1-1-111-1-1111-11111-1-1-1-11-1-1-111-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−ii
χ1111-1-1111-111-1-1-1-111-11-11-11111-1-1111-1-1-1-1-1-111-1-1111-11111-1-1-1-11-1-1-111-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i−i−iii−ii
χ1211-1-1111-111-1-1-1-111-11-11-11111-1-1111-1-1-1-1-1-111-1-1111-11111-1-1-1-11-1-1-111-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iiiii−i−ii−i
χ1311-1-1111-111-1-1-1-11-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-1-1-1-111i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111−i−iiii−i
χ1411-1-1111-111-1-1-1-11-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-1-1-1-111i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1ii−i−i−ii
χ1511-1-1111-111-1-1-1-11-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-1-1-1-111−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111ii−i−i−ii
χ1611-1-1111-111-1-1-1-11-111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11-1-1-1-111−iii−i-111-1−i−iiiii−i−i-1-11111-1-1−i−iiii−i
χ1722222222222222-22-22-2-222222-2-2222222222-2-222-2-22-2-2-222-2-2-2-2-22-2-2-2-222000000000000000000000000000000
χ1822222222222222-2-222-22-222-2-22222222222222-2-2-2-2-22-2-2-2-222-2-22-2-2-222-2-2000000000000000000000000000000
χ19222222-122-122-1-1222-12222-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12-12-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ20222222-122-122-1-1222-12222-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-12-1-1-1-1-1-12-12-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ21222222-122-122-1-12-2-2-12-2-22-1-2-211-1-1-12-1-1-1-1-111-2-22-11-2-1-111112-1-21-1-111112i2i−2i−2i0000−i−i−i−iiiii00000000000000
χ22222222-122-122-1-12-2-2-12-2-22-1-2-211-1-1-12-1-1-1-1-111-2-22-11-2-1-111112-1-21-1-11111−2i−2i2i2i0000iiii−i−i−i−i00000000000000
χ23222222-122-122-1-1-22-2-1-2-222-12211-1-1-12-1-1-1-1-11122-21-1-211-1-111-21-2-11111-1-1000000003−33−33−33−300000000000000
χ24222222-122-122-1-1-22-2-1-2-222-12211-1-1-12-1-1-1-1-11122-21-1-211-1-111-21-2-11111-1-100000000−33−33−33−3300000000000000
χ25222222-122-122-1-1-2-22-1-22-22-1-2-2-1-1-1-1-12-1-1-1-1-1-1-1-2-2-21121111-1-1-212111-1-11100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ26222222-122-122-1-1-2-22-1-22-22-1-2-2-1-1-1-1-12-1-1-1-1-1-1-1-2-2-21121111-1-1-212111-1-11100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ2722222-122-12-1-122222-1222-12-1-122-1-1-1-12-1-1-1-122-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ2822222-122-12-1-122222-1222-12-1-122-1-1-1-12-1-1-1-122-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ2922222-122-12-1-1222-2-2-12-2-2-1211-2-2-1-1-1-12-1-1-1-1-2-211-12-21-1-11111-121-2-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii000000
χ3022222-122-12-1-1222-2-2-12-2-2-1211-2-2-1-1-1-12-1-1-1-1-2-211-12-21-1-11111-121-2-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i000000
χ3122222-122-12-1-122-22-2-1-2-22-12-1-1-2-2-1-1-1-12-1-1-1-1-2-2-1-11-22111-1-1111-2121111-1-10000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ3222222-122-12-1-122-22-2-1-2-22-12-1-1-2-2-1-1-1-12-1-1-1-1-2-2-1-11-22111-1-1111-2121111-1-10000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ3322222-122-12-1-122-2-22-1-22-2-121122-1-1-1-12-1-1-1-122111-2-2-11111-1-11-2-1-211-1-11100000000000000003−33−3−33−33000000
χ3422222-122-12-1-122-2-22-1-22-2-121122-1-1-1-12-1-1-1-122111-2-2-11111-1-11-2-1-211-1-1110000000000000000−33−333−33−3000000
χ3522-2-2222-222-2-2-2-2-22222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2000000000000000000000000000000
χ3622-2-2222-222-2-2-2-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000000000
χ3722-2-222-1-22-1-2-21122-2-1-22-22-12211-1-1-1-211111-1-1-2-22-1-1-2-1-1-1-111-212111-1-1112-22-20000-1-111-1-11100000000000000
χ3822-2-222-1-22-1-2-21122-2-1-22-22-12211-1-1-1-211111-1-1-2-22-1-1-2-1-1-1-111-212111-1-111-22-22000011-1-111-1-100000000000000
χ3922-2-222-1-22-1-2-2112-22-1-2-222-1-2-2-1-1-1-1-1-21111111222-112-1-111-1-1-21-2-11111-1-12i−2i−2i2i0000−i−iiiii−i−i00000000000000
χ4022-2-222-1-22-1-2-2112-22-1-2-222-1-2-2-1-1-1-1-1-21111111222-112-1-111-1-1-21-2-11111-1-1−2i2i2i−2i0000ii−i−i−i−iii00000000000000
χ4122-2-222-1-22-1-2-211-222-12-2-22-122-1-1-1-1-1-21111111-2-2-21-1211-1-1-1-12-1-21-1-11111000000003−3−333−3−3300000000000000
χ4222-2-222-1-22-1-2-211-222-12-2-22-122-1-1-1-1-1-21111111-2-2-21-1211-1-1-1-12-1-21-1-1111100000000−333−3−333−300000000000000
χ4322-2-222-1-22-1-2-211-2-2-2-12222-1-2-211-1-1-1-211111-1-122-211-21111112-12-1-1-1-1-1-1-100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ4422-2-222-1-22-1-2-211-2-2-2-12222-1-2-211-1-1-1-211111-1-122-211-21111112-12-1-1-1-1-1-1-100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ4522-2-22-12-2-1211-2-222-2-1-22-2-12-1-1-2-2-1-1-11-211112211-1221-1-1-1-1111-2-1-211-1-11100002i−2i2i−2i00000000−i−iii−i−iii000000
χ4622-2-22-12-2-1211-2-222-2-1-22-2-12-1-1-2-2-1-1-11-211112211-1221-1-1-1-1111-2-1-211-1-1110000−2i2i−2i2i00000000ii−i−iii−i−i000000
χ4722-2-22-12-2-1211-2-22-22-1-2-22-121122-1-1-11-21111-2-2-1-1-12-2-1-1-111-1-11-2121111-1-100002-2-2200000000-1-11111-1-1000000
χ4822-2-22-12-2-1211-2-22-22-1-2-22-121122-1-1-11-21111-2-2-1-1-12-2-1-1-111-1-11-2121111-1-10000-222-20000000011-1-1-1-111000000
χ4922-2-22-12-2-1211-2-2-222-12-2-2-12-1-122-1-1-11-21111-2-2111-22-111-1-1-1-1-121-2-1-1111100000000000000003−3−333−3−33000000
χ5022-2-22-12-2-1211-2-2-222-12-2-2-12-1-122-1-1-11-21111-2-2111-22-111-1-1-1-1-121-2-1-111110000000000000000−333−3−333−3000000
χ5122-2-22-12-2-1211-2-2-2-2-2-1222-1211-2-2-1-1-11-2111122-1-11-2-21111111-12-12-1-1-1-1-1-10000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ5222-2-22-12-2-1211-2-2-2-2-2-1222-1211-2-2-1-1-11-2111122-1-11-2-21111111-12-12-1-1-1-1-1-10000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ5344444-2-24-2-2-2-2-2-24441444-2-2-2-2-2-2111-2-21111-2-2-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000
χ5444444-2-24-2-2-2-2-2-24-4-414-4-4-2-22222111-2-211112222-2-22211-1-1-1-1-2-22211-1-1-1-1000000000000000000000000000000
χ5544444-2-24-2-2-2-2-2-2-44-41-4-44-2-2-2-222111-2-2111122-2-222-22-1-111-1-1222-2-1-1-1-111000000000000000000000000000000
χ5644444-2-24-2-2-2-2-2-2-4-441-44-4-2-222-2-2111-2-21111-2-222222-2-1-1-1-11122-22-1-111-1-1000000000000000000000000000000
χ574444-444-44444440004000-4-40000-4-44-4-444-4-4000000000000000000000000000000000000000000000000000000
χ584444-44-2-44-244-2-2000-2000-4200−2i32i322-2-42-2-222−2i32i30000000000−2i32i3000000−2i32i300000000000000000000000000000000
χ594444-44-2-44-244-2-2000-2000-42002i3−2i322-2-42-2-2222i3−2i300000000002i3−2i30000002i3−2i300000000000000000000000000000000
χ604444-4-24-4-24-2-244000-20002-4−2i32i30022-22-4-2-22200−2i32i3000000−2i32i30000000000−2i32i3000000000000000000000000000000
χ614444-4-24-4-24-2-244000-20002-42i3−2i30022-22-4-2-222002i3−2i30000002i3−2i300000000002i3−2i3000000000000000000000000000000
χ624444-4-2-2-4-2-2-2-2-2-2000100022−2i32i3−2i32i3-1-112211-1-1−2i32i3−2i32i300003-3i3−i3i3−i300003-3i3−i3i3−i3000000000000000000000000000000
χ634444-4-2-2-4-2-2-2-2-2-2000100022−2i32i32i3−2i3-1-112211-1-12i3−2i3−2i32i30000-33i3−i3−i3i30000-33−i3i3i3−i3000000000000000000000000000000
χ644444-4-2-2-4-2-2-2-2-2-20001000222i3−2i3−2i32i3-1-112211-1-1−2i32i32i3−2i30000-33−i3i3i3−i30000-33i3−i3−i3i3000000000000000000000000000000
χ654444-4-2-2-4-2-2-2-2-2-20001000222i3−2i32i3−2i3-1-112211-1-12i3−2i32i3−2i300003-3−i3i3−i3i300003-3−i3i3−i3i3000000000000000000000000000000
χ6644-4-44-2-2-4-2-2222244-41-44-4-2-2-2-22211122-1-1-1-1-2-222-2-2-221111-1-122-22-1-111-1-1000000000000000000000000000000
χ6744-4-44-2-2-4-2-222224-441-4-44-2-222-2-211122-1-1-1-122-2-2-2-22-211-1-111222-2-1-1-1-111000000000000000000000000000000
χ6844-4-44-2-2-4-2-22222-44414-4-4-2-2-2-2-2-211122-1-1-1-1222222-2-2-1-11111-2-22211-1-1-1-1000000000000000000000000000000
χ6944-4-44-2-2-4-2-22222-4-4-41444-2-2222211122-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000
χ7044-4-4-444444-4-4-4-40004000-4-40000-4-4444-4-444000000000000000000000000000000000000000000000000000000
χ7144-4-4-44-244-2-4-422000-2000-4200−2i32i322-24-222-2-22i3−2i30000000000−2i32i30000002i3−2i300000000000000000000000000000000
χ7244-4-4-44-244-2-4-422000-2000-42002i3−2i322-24-222-2-2−2i32i300000000002i3−2i3000000−2i32i300000000000000000000000000000000
χ7344-4-4-4-244-2422-4-4000-20002-4−2i32i30022-2-2422-2-2002i3−2i3000000−2i32i300000000002i3−2i3000000000000000000000000000000
χ7444-4-4-4-244-2422-4-4000-20002-42i3−2i30022-2-2422-2-200−2i32i30000002i3−2i30000000000−2i32i3000000000000000000000000000000
χ7544-4-4-4-2-24-2-22222000100022−2i32i3−2i32i3-1-11-2-2-1-1112i3−2i32i3−2i30000-33i3−i3i3−i300003-3−i3i3−i3i3000000000000000000000000000000
χ7644-4-4-4-2-24-2-22222000100022−2i32i32i3−2i3-1-11-2-2-1-111−2i32i32i3−2i300003-3i3−i3−i3i30000-33i3−i3−i3i3000000000000000000000000000000
χ7744-4-4-4-2-24-2-222220001000222i3−2i3−2i32i3-1-11-2-2-1-1112i3−2i3−2i32i300003-3−i3i3i3−i30000-33−i3i3i3−i3000000000000000000000000000000
χ7844-4-4-4-2-24-2-222220001000222i3−2i32i3−2i3-1-11-2-2-1-111−2i32i3−2i32i30000-33−i3i3−i3i300003-3i3−i3i3−i3000000000000000000000000000000
χ794-44i−4i0440-4-44i−4i4i−4i000400000000000-4004i−4i000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ804-44i−4i0440-4-44i−4i4i−4i000400000000000-4004i−4i00000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ814-4−4i4i0440-4-4−4i4i−4i4i000400000000000-400−4i4i00000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ824-4−4i4i0440-4-4−4i4i−4i4i000400000000000-400−4i4i000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ838-88i−8i08-40-848i−8i−4i4i000-400000000000400−4i4i00000000000000000000000000000000000000000000000000000000
χ848-88i−8i0-4804-8−4i4i8i−8i000-400000000000400−4i4i00000000000000000000000000000000000000000000000000000000
χ858-88i−8i0-4-4044−4i4i−4i4i00020000000006-6-2002i−2i6i−6i000000000000000000000000000000000000000000000000000000
χ868-88i−8i0-4-4044−4i4i−4i4i0002000000000-66-2002i−2i−6i6i000000000000000000000000000000000000000000000000000000
χ878-8−8i8i08-40-84−8i8i4i−4i000-4000000000004004i−4i00000000000000000000000000000000000000000000000000000000
χ888-8−8i8i0-4804-84i−4i−8i8i000-4000000000004004i−4i00000000000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4-40444i−4i4i−4i00020000000006-6-200−2i2i−6i6i000000000000000000000000000000000000000000000000000000
χ908-8−8i8i0-4-40444i−4i4i−4i0002000000000-66-200−2i2i6i−6i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.